Answer to Question #87906 in Mechanics | Relativity for Ghada Albader

Question

Pistons are free to move in two cylinders which are connected by a hydraulic fluid. The area of the smaller piston is 1.2 cm2. A force of 150 N on this piston will move a weight of 2700 N on the larger piston. (Assume that friction is negligible.)
A) What is the area of the large piston?
B) What is the pressure in the fluid? (Give answer in Pascals)

Answer 1

A) We can find the area of the large piston from the hydraulic press formula:

$$\dfrac{F_1}{A_1} = \dfrac{F_2}{A_2},$$

here, $F_1$ is the force that acts on the smaller piston, $F_2$ is the force that acts on the larger piston, $A_1$ is the area of the smaller piston, $A_2$ is the area of the larger piston.

Then, from this formula we can calculate the area of the large piston:

$$A_2 = A_1 \dfrac{F_2}{F_1} = 1.2 cm^2 \cdot \dfrac{1m^2}{10^4 cm^2} \cdot \dfrac{2700 N}{150 N} = 22 \cdot 10^{-4} m^2.$$

B) We can find the pressure in the fluid from the formula:

$$P = \dfrac{F_1}{A_1} = \dfrac{150 N}{1.2 cm^2 \cdot \dfrac{1m^2}{10^4 cm^2}} = 1.25 \cdot 10^6 Pa.$$

Answer:

A) $A_2 = 22 \cdot 10^{-4} m^2.$

B) $P = 1.25 \cdot 10^6 Pa.$